Large Grants

Mini-Grants

Oregon State University

Co-Investigators

Corinne A. Manogue,

*Department of Physics, Oregon State University*

Project Title

Using Octonionic Cayley Spinors to Describe Fundamental Particles

Project Summary

How many dimensions are there in the universe? Could any "extra" dimensions represent the Standard Model? An underlying principle is needed to answer these and similar questions. We believe the key is to reformulate existing theory in terms of two special mathematical structures: the octonions -- the largest division algebra, and the exceptional Jordan algebra -- the largest reasonable matrix algebra over the octonions. For 20 years, we have been carefully examining how to rewrite certain pieces of fundamental physical theories in terms of these structures. It turns out that this can be done only in special cases. For example, Lorentz transformations exist in any dimension, but only in ten dimensions do they fit naturally inside the exceptional Jordan algebra. Every time we have used the octonions to guide our choices, we have discovered new features of these special cases. Instead of being inputs to the theory, motivated by experiment, these facts emerge naturally as consequences of the special properties of these mathematical structures. We plan to explore the tantalizing evidence that these mathematical structures can be used to give a unified theory of fundamental particles and their interactions.

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